https://www.chenk.top/en/tags/homomorphisms/Recent content in Homomorphisms on Chen Kai BlogHugoenSun, 05 Sep 2021 09:00:00 +0000https://www.chenk.top/en/abstract-algebra/03-quotient-groups-and-homomorphisms/Sun, 05 Sep 2021 09:00:00 +0000https://www.chenk.top/en/abstract-algebra/03-quotient-groups-and-homomorphisms/<p>A group can be enormous &mdash; millions of elements, intricate multiplication tables, symmetries that take pages to describe. Yet hidden inside every group are natural compression points where you can collapse entire chunks of the group into single elements, producing a smaller group that still remembers something essential about the original. This article develops the machinery for doing that: normal subgroups, quotient groups, homomorphisms, and the isomorphism theorems that tie everything together.</p>